BAGHDAD, Iraq (CNN) -- As many as a dozen U.S. Marines were killed Tuesday in heavy fighting in the western Iraq town of Ramadi, the latest in a series of clashes with anti-coalition elements, Pentagon officials said.

East of Ramadi, heavy fighting was reported in the Sunni enclave of Fallujah as Marines and Iraqi security forces were reasserting control after the killing and mutilation of four civilian security guards last week.

And in Baghdad and at least four cities in the country's south, U.S. and coalition troops battled supporters of Shiite Muslim cleric Muqtada al-Sadr for a third day.

The Marine deaths in Ramadi and that of a soldier in a Baghdad rocket-propelled grenade attack made Tuesday one of the deadliest days for American troops in Iraq since President Bush declared the end of major combat on May 1.

Eighteen Americans were killed November 15, most of them in the collision of two Black Hawk helicopters shot down in Mosul. Sixteen U.S. troops were killed November 2 when an Army Chinook helicopter was shot down near Fallujah.

In the holy city of Najaf in southern Iraq, al-Sadr's militia was in control of government, police and spiritual sites, a coalition source said.

Al-Sadr also was busing followers into Najaf from Sadr City, a Baghdad neighborhood, according to the coalition source, who said that many members of his outlawed militia, Mehdi's Army, were from surrounding provinces.

Al-Sadr -- who is wanted on murder charges in connection with the killing of a rival last year -- reportedly has taken refuge in the Imam Ali mosque in Najaf, one of Shiite Islam's holiest shrines.

A posting on al-Sadr's Web site said he has called for a general strike.

Qais al-Khazaal, a spokesman for al-Sadr, said the young cleric wants coalition troops to withdraw from populated areas and release prisoners taken into custody in recent demonstrations.

Marines moved into Fallujah from several directions -- coming under heavy fire from insurgents -- in a second day of an operation to lock down the city.

Fighting broke out between coalition forces and al-Sadr's Mehdi Army on Saturday after the arrest of the cleric's deputy on charges in connection with Abdul Majeed al-Khoei's death April 10, 2003, outside the Imam Ali shrine in Najaf.

Twelve people were arrested last fall when an Iraqi judge issued 25 warrants in the case, including the ones for al-Sadr and his deputy, Mustafa al-Yaqoubi, coalition officials said.

Yaqoubi was arrested Saturday in Najaf and turned over to Iraqi police Monday, they said.

About 50 Iraqis were reported killed around the country in Tuesday's clashes.

Hospital sources said 36 of those were killed in battles with U.S. troops in Baghdad's Sadr City, a Shiite slum named for the rebellious cleric's assassinated father.

Bremer described al-Sadr as "a guy who has a fundamentally inappropriate view of the new Iraq."

"He believes that in the new Iraq, like in the old Iraq, power should be to the guy with guns," Bremer said. "That is an unacceptable vision for Iraq."

"Sistani said in his letter that he supported us for standing for what we believe ... but that he also thought that we should try to resolve this matter in a more calm and civil way,"al-Khazaal said.

Pentagon sources said the military would exercise caution in seeking al-Sadr in an attempt to avoid giving him more stature among radicalized Iraqis.

Pentagon officials played down reports that American troops' tours of duty in Iraq could be extended to bolster the U.S. occupation force there.

Though that is one possibility, one official said it was not under "active consideration." (Full story)

About 134,000 U.S. troops are now in Iraq, but that number is scheduled to drop to 110,000 over the next few months as part of a scheduled rotation of forces.

Other developments

Since the start of the war last year, 624 U.S. troops have died, 434 of them in hostile action. Since May 1, 315 U.S. troops have been killed in hostile action.

Britain is sending thousands of troops to Iraq to replace those already serving there, said Maj. Rachel Grimes of the Ministry of Defense. She said the move was part of a "normal" six-month rotation and would not result in an increase in the number of British troops in Iraq.